Opposition groups had called for a boycott, arguing that the vote would allow Aliyev, whose family has dominated politics in Azerbaijan for nearly four decades, to be president for life.
However, more than 71 per cent of voters in the Muslim majority country of 8.7 million turned out, the election commission said.
|Azerbaijan has immensely profited from its vast oil and gas reserves
Aliyev won a second five-year term last October, having taken over from his father Heydar, a top-ranking former Soviet official, in 2003.
Heydar Aliyev was a Soviet-era leader and president for 10 years after the country won independence in 1991.
The younger Aliyev was first elected to replace his father shortly before the 80-year-old's death.
Supporters of the changes insisted they are aimed at making Azerbaijan more democratic by allowing voters to choose whoever they wish to be president.
But critics say the vote was aimed at consolidating the grip of the first family.
Many of Azerbaijan's main opposition accused the authorities of preparing to fix the vote, harassing opposition campaigners and using government control of the media to dominate the debate.
Ali Keremli, leader of the anti-government National Front party, said opposition monitors had seen numerous voting violations on Wednesday.
At polling stations in the capital Baku many voters said they supported the move and credited Aliyev with steering the country through a period of record economic growth.
"I voted so that Ilham Aliyev may continue to be our president because he has brought us stability," Khatima Jabrailova, a 72-year-old pensioner, told AFP news agency.
But some said the two-term limit should stand.
"I voted against this. There is no need to change our constitution," said Vugar Shabalov, a 21-year-old student.
"In a time when the whole world is in economic crisis, we should not be spending money on this referendum."
Despite opposition objections, the referendum has drawn little criticism from the United States or European countries.
Azerbaijan's opposition accuses Western governments of shying away from criticising Aliyev to secure access to Azerbaijan's vast Caspian Sea oil and gas reserves.